This thesis examines the heating of the solar atmosphere due to energy release in solar flares. A one-dimensional hydrodynamic model, which solves the equations of conservation of mass, momentum, and energy along a magnetic flux tube, is described in detail and employed to study the dynamic response of the solar atmosphere to large amounts of energy release from the magnetic field.

A brief introduction to the solar atmosphere and solar flares, from both observational and theoretical perspectives, is given. Then, the hydrodynamic model is described, along with derivations of energy deposition due to a beam of highly energetic electrons colliding with the ambient atmosphere (and their implementation in the model is explained). Using this model of heating along with RHESSI-derived parameters of observed flares, the sensitivity of the GOES flare classification to the parameters of the electron beam (the non-thermal energy, the power-law index of the electron distribution, and the low-energy cut-off) are examined, and clear correlations are determined.

Next, the response of the atmosphere to heating due to isoenergetic beams of electrons are studied, to elucidate the importance of electrons at different energy. It is found that at high total energy fluxes, the energy of individual electrons are unimportant, but that at lower fluxes, lower energy electrons are significantly more efficient at heating the atmosphere and driving chromospheric evaporation than high energy electrons. It is also found that the threshold for explosive evaporation is strongly dependent on the cut-off energy, as well as the beam flux. A case study of a well-observed flare is performed. The flare, a C-class flare that occurred on 28 November 2002, was modeled for various cases of heating due to a beam of electrons, in situ coronal heating, and a hybrid model that combines both forms of heating. It is found that the observation of X-ray source heights seen with RHESSI are most consistent with a hybrid model. The results indicate that the energy must be partitioned between thermal and kinetic energy, and the implications are discussed.

This work is then summarized, and future avenues of research are discussed. Improvements that can be made to the model, the forward modeling of emission, and comparisons to observations are discussed.